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Simplifying -2s2 + -9s + -8 = 0 Reorder the terms: -8 + -9s + -2s2 = 0 Solving -8 + -9s + -2s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 9s + 2s2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 9s + 2s2)' equal to zero and attempt to solve: Simplifying 8 + 9s + 2s2 = 0 Solving 8 + 9s + 2s2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 4.5s + s2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.5s + -4 + s2 = 0 + -4 Reorder the terms: 4 + -4 + 4.5s + s2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.5s + s2 = 0 + -4 4.5s + s2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.5s + s2 = -4 The s term is 4.5s. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5s + 5.0625 + s2 = -4 + 5.0625 Reorder the terms: 5.0625 + 4.5s + s2 = -4 + 5.0625 Combine like terms: -4 + 5.0625 = 1.0625 5.0625 + 4.5s + s2 = 1.0625 Factor a perfect square on the left side: (s + 2.25)(s + 2.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (s + 2.25) equal to 1.030776406 and -1.030776406.Subproblem 1
s + 2.25 = 1.030776406 Simplifying s + 2.25 = 1.030776406 Reorder the terms: 2.25 + s = 1.030776406 Solving 2.25 + s = 1.030776406 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + s = 1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + s = 1.030776406 + -2.25 s = 1.030776406 + -2.25 Combine like terms: 1.030776406 + -2.25 = -1.219223594 s = -1.219223594 Simplifying s = -1.219223594Subproblem 2
s + 2.25 = -1.030776406 Simplifying s + 2.25 = -1.030776406 Reorder the terms: 2.25 + s = -1.030776406 Solving 2.25 + s = -1.030776406 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + s = -1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + s = -1.030776406 + -2.25 s = -1.030776406 + -2.25 Combine like terms: -1.030776406 + -2.25 = -3.280776406 s = -3.280776406 Simplifying s = -3.280776406Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.219223594, -3.280776406}Solution
s = {-1.219223594, -3.280776406}
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